Discrete Tomography of Mathematcal Quasicrystals: A Primer

This text is a report on work progress. We introduce the class of cyclotomic model sets (mathematical quasicrystals) Λ ⊂ Z [ ξ n ] , where Z [ ξ n ] is the ring of integers in the nth cyclotomic field Q ( ξ n ) , and discuss the corresponding decomposition, consistency and reconstruction problems of the discrete tomography of these sets. Our solution of the so-called decomposition problem also applies to the case of the square lattice Z 2 = Z [ ξ 4 ] , which corresponds to the classical setting of discrete tomography.